Basic density-functional perturbation

Basic Equations of Density-functional Perturbation Theory... 

Today we know that the HF method gives a very precise description of the electronic structure for most closed-shell molecules in their ground electronic state. The molecular structure and physical properties can be computed with only small errors. The electron density is well described. The HF wave function is also used as a reference in treatments of electron correlation, such as perturbation theory (MP2), configuration interaction (Cl), coupled-cluster (CC) theory, etc. Many semi-empirical procedures, such as CNDO, INDO, the Pariser-Parr-Pople method for rr-eleetron systems, ete. are based on the HF method. Density functional theory (DFT) can be considered as HF theory that includes a semiempirical estimate of the correlation error. The HF theory is the basie building block in modern quantum chemistry, and the basic entity in HF theory is the moleeular orbital. 

Subsequent papers by Cremer and Grafenstein have been devoted to analysis of basic electronic effects on the spin-spin coupling by the use of coupled perturbed density-functional theory combined with the recently developed J-OC-PSP (decomposition of J into orbital contributions using orbital currents and partial spin polarization). Among others, one-bond H-C and two-bond H-H couplings have been analysed for methane. 

To aid the choice of the most appropriate method, we can briefly classify the presently available approaches for the treatment of molecular excitations into few main groups. In the following the reader is supposed to be familiar with the basics of the Hartree-Fock method [33], density functional theory [73, 74], and perturbation theory [33]. 

Theoretical determinations are mainly based on the assumption that the initial perturbation of the orbital of interacting species determines the course of a reaction or an interaction. In terms of equation of state, the perturbation theory was developed first. In terms of energy gap between HOMO and LUMO, acids and bases were defined by their hardness and softness. The Hard-Soft Acid-Base principle (Pearson 1963) describes some basic rules about kinetics and equilibrium of the acid-base interactions. The HSAB principle will be described as it has evolved in recent years on the basis of the density-functional theory (Parr and Yang 1989). For organic interactions, the following statements were proposed ... 

The effect of external field on reactivity descriptors has been of recent interest. Since the basic reactivity descriptors are derivatives of energy and electron density with respect to the number of electrons, the effect of external field on these descriptors can be understood by the perturbative analysis of energy and electron density with respect to number of electrons and external field. Such an analysis has been done by Senet [22] and Fuentealba [23]. Senet discussed perturbation of these quantities with respect to general local external potential. It can be shown that since p(r) = 8E/8vexl, Fukui function can be seen either as a derivative of chemical potential... 

A second and more widely used approach for the computation of excitation energies within DFT is based on the linear-response formulation of the time-dependent perturbation of the electronic density. The basic quantity in linear response TDDFT (LR-TDDFT) is the time-dependent density-density response function [33]... 

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